The article "Physical Properties of Cumin Seed" (J. of Agric. Engr. Res., 1996: 93-98) considered a quadratic regression of y 5 bulk density on x 5 moisture content. Data from a graph in the article follows, along with Minitab output from the quadratic fit.

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a. Does a scatterplot of the data appear consistent with the quadratic regression model?
b. What proportion of observed variation in density can be attributed to the model relationship?
c. Calculate a 95% CI for true average density when moisture content is 13.7.
d. The last line of output is from a request for estimation and prediction information when moisture content is 14. Calculate a 99% PI for density when moisture content is 14.
e. Does the quadratic predictor appear to provide useful information? Test the appropriate hypotheses at significance level .05.

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The regression equation is bulkdens403 16.2 moiscont -0.706 contsqd Predictor Constant moiscont contsqd S-10.15 Coef 403.24 16.164 -0.7063 StDev 36.45 5.451 0.1852 11.060.002 2.970.059 -3.81 0.032 R-S-93 . 8% R-Sg(adj )-89. 6% Analysis of Variance Source Regression Residual Error 3 309.1 103.0 Total DF MS 2 4637.7 2318.9 22.51 0.016 5 4946.8 StDev St Fit Fit Residual Resid 7.0479.00 481.78 9.35 -2. 78 -0.70 8.21 0.98 13.7 487.00 492.12 6.49 -5.12 -0.66 16.6 470.00 476.93 6.10 -6.93 -0.85 19.8 458.00 446.39 5.69 11.61 1.38 22.0 412.00 416.99 8.75 -4.99 -0.97 obs moiscont bulkdens 1 10.3 503.00 494.79 5.78 4 StDev Fit Fit 95.0% CI 95.0% PI 491.10 6.52 (470.36, 511.83) 452.71, 529.48)